• Journal of applied mathematics & informatics
• /
• 제10권1_2호
• /
• pp.101-109
• /
• 2002

We extend two inequalities involving Hadamard Products of Positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods we different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458-463(2000)] and B.-Y Wang et al in [Lin. Alg. Appl. 302-303: 163-172(1999)] .

• 대한수학회보
• /
• 제44권4호
• /
• pp.597-606
• /
• 2007

The object of the present paper is to show quasi-Hadamard products of certain p-valent functions with negative coefficients in the open unit disc. Our results are the generalizations of the corresponding results due to Yaguchi et al. [10], Aouf and Darwish [3], Lee et al. [5] and Sekine and Owa [9].

• 대한전자공학회논문지
• /
• 제24권1호
• /
• pp.173-176
• /
• 1987

This paper presents a simple factorization of the Hadamard matrix which is used to develop a fast algorithm for the Hadamard transform. This matrix decomposition is of the kronecker products of identity matrices and successively lower order Hadamard matrices. This following shows how the Kronecker product can be mathematically defined and efficiently implemented using a factorization matrix methods.

• 대한수학회보
• /
• 제37권3호
• /
• pp.633-639
• /
• 2000

Let $A=(a_{ij}\ and\ B=(b_{ij}\ be\ n\times\ n$ complex matrices and let A$\bigcirc$B denote the Hadamard product of A and B, that is $AA\circB=(A_{ij{b_{ij})$.We conjecture a permanental analog of Oppenheim's inequality and verify it for n=2 and 3 as well as for some infinite classes of matrices.

• 대한수학회논문집
• /
• 제29권1호
• /
• pp.51-63
• /
• 2014

In the paper, several properties of geometric-arithmetically s-convex functions are provided, an integral identity in which the integrands are products of a function and a derivative is found, and then some inequalities of Hermite-Hadamard type for integrals whose integrands are products of a derivative and a function whose derivative is of the geometric-arithmetic s-convexity are established.

• 대한수학회지
• /
• 제19권2호
• /
• pp.75-82
• /
• 1983

• Kyungpook Mathematical Journal
• /
• 제29권1호
• /
• pp.7-10
• /
• 1989

• Kyungpook Mathematical Journal
• /
• 제57권4호
• /
• pp.641-649
• /
• 2017

For partitioned matrices, the Khatri-Rao product is viewed as a generalized Hadamard product. In this paper we present Oppenheim's and Schur's determinantal inequalities for the Khatri-Rao product of two positive semidefinite matrices.

• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.125-133
• /
• 2002

Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.

• 대한수학회보
• /
• 제41권1호
• /
• pp.53-71
• /
• 2004

A certain subclass $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ of starlike functions in the unit disk is introduced. The object of the present paper is to derive several interesting properties of functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$. Coefficient inequalities, distortion theorems and closure theorems of functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ are determined. Also we obtain radii of convexity for the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$. Furthermore, integral operators and modified Hadamard products of several functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ are studied here.